Thermal Expansion Properties - Solid State Physics - Lecture Slides, Slides of Solid State Physics

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Scientists do stupid looking things sometimes (though not too

unsafe if they made the material carefully enough)

- Materials change size when heating.

L^

final

L

initial

L^

initial

(T

final

T

initial

CTE: coefficient ofthermal expansion (units: 1/K)

Tinit Tfinal

Linit Lfinal

THERMAL EXPANSION

• Melting Temperature, T

m r

smaller Tmlarger Tm

Energy (r)

r^ o

T

m^

is larger if E

o^

is larger.

PROPERTIES FROM BONDING: T

M

• Elastic modulus, E• E ~ curvature at r

o

crosssectionalarea Ao

 L

length, Lo

F

undeformed

deformed

 L

F A

= E o

Lo Elastic modulus

r

larger Elastic Modulus

smaller Elastic Modulus

Energy

unstretched lengthr^ o

E is larger if curvature is larger.

PROPERTIES FROM BONDING:

Elastic Properties

E similar to spring constant

T^0

T T 2 3

Atomic positions and vibrations

-^

The minimum in an atomic energyvs. interatomic distance curveyields the

near neighbor distance

(bond length).

-^

The width of the curve is proportional to the amplitude ofthermal vibrations for an atom

.

-^

If the curve is symmetric, there isno shift in the average position ofthe atom (the center of the thermalvibrations at any given T).

-^

The coefficient of thermalexpansion is negligible forsymmetric energy wells.

Thermal Expansion

•^

If the curve is not symmetric, the average position in whichthe atom sits shifts with temperature.

-^

Bond lengths therefore change (usually get bigger forincreased T).

-^

Thermal expansion coefficient is nonzero.

Bond energy

Bond length (r)

increasing T

T

r(T5)

r(T1)

T

bond energy vs bond lengthcurve is “asymmetric”

Thermal expansion example

•^

Example

-^

An Al wire is 10 m long and is cooled from 38 to -1 degreeCelsius. How much change in length will it experience?



l = l

o



l

T

= (10 m) 23.6 x 10

^6

(

C)

^1

C



38

C)

-9.2 mm

Small/Negative thermal expansion

•^

Invar (Ni-Fe alloy) is the most common low thermal expmaterial:

α

/ degree

•^

Some materials have

α

<0 in one dimension and >0 in others.

•^

It is possible, though not intuitive, for materials to have anegative thermal expansion in all dimensions.– An increase in temperature causes the crystal to shrink.

-^

ZrW

O 2

: contracts continuously and linearly from 2 to 1050K 8

-^

Composites could allow zero thermal expansion components (superb foroptics, engine parts, etc).

http://www.dur.ac.uk/john.evans/webpages/research_nteintro.html

HEAT CAPACITY

K

J/mol(

(^

e

temperatur

d

energy

d

dQdT

C

Capacity at constant volume =

C

V

Capacity at constant pressure =

C

P

C

P^

is typically >

C

, but the difference is small for solids. V

When heated, materials experience an increase in T. Thismeans that heat is absorbed.Heat capacity represents the amount of energy required toproduce a unit temperature rise.

2

4.18 J raises 1g of H O by 1 K4.18 J raises 1g of Cu by 11 K

H

O has a higher heat capacity 2

HEAT CAPACITY – The Dulong-Petit Law

N

k 0

b

V^

o^

B

C

of

N k

 D

=Temperature at which

 D

(Cu)

 D

(Al)

 D

(Pb)

T2 > T

T

x

x

heat flux

THERMAL CONDUCTIVITY

^

^

2

nd

2

'^

L

T^

T^

T^

T

k^

if K

f^

T

k^

Fick s

aw

t^

x^

x^

t^

x ^

^

^

^

^

^

^

^

^

^

^

^

^

^

^

^

^

^

Fick’s Second Law

- Non-Steady State:

dT/dt is not constant.

- Polymers

PolypropylenePolyethylenePolystyreneTeflon

0.120.46-0.500.130.

k (W/m-K)

- Ceramics

Magnesia (MgO)Alumina (Al2O3)Soda-lime glassSilica (cryst. SiO2)

3839 1.71.

- Metals

AluminumSteelTungstenGold

24752178315

increasing k

Energy TransferBy vibration ofatoms andmotion ofelectronsBy vibration ofatoms By vibration/rotation of chainmolecules

Material

Selected values from Table 19.1,

Callister 6e.

K=k

+kl

:^ e

Again think about band gaps: metals have lots of free electrons(k

is large), while ceramics have few (only ke^

is active).l^

THERMAL CONDUCTIVITY

•^

Thermal conductivity istemperature dependent.– Analagous to electron

scattering.

• Usually first decreases with

increasing temperature•

Higher Temp=more scatteringof electrons AND phonons,thus less transfer of heat.

• Then increases at still higher

temperatures due to otherprocesses we haven‘tconsidered in this class(radiative heat transfer—eg. IRlamps).

THERMAL CONDUCTIVITY

Thermal conductivity optimization

To maximize thermal conductivity, there are several options:

• Provide as many free electrons (in the conduction band) as possible -^

free electrons conduct heat more efficiently than phonons.

• Make crystalline instead of amorphous -^

irregular atomic positions in amorphous materials scatter phonons anddiminish thermal conductivity

• Remove grain boundaries -^

gb’s scatter electrons and phonons that carry heat

• Remove pores (air is a terrible conductor of heat)